# Winter's formula

Winters' formula,[1] named for Dr. R.W. Winters,[2] is a formula used to evaluate respiratory compensation when analyzing acid–base disorders and a metabolic acidosis is present.[3][4] It can be given as

,

where HCO3 is given in units of mEq/L and pCO2 will be in units of mmHg.

Winters' formula gives an expected value for the patient's PCO2; the patient's actual (measured) PCO2is then compared to this:

• If the two values correspond, respiratory compensation is considered to be adequate.
• If the measured PCO2 is higher than the calculated value, there is also a primary respiratory acidosis.
• If the measured PCO2 is lower than the calculated value, there is also a primary respiratory alkalosis.

## Alkalosis

Note that Winter's formula pertains to settings of metabolic acidosis.

To calculate the expected pCO2 in the setting of metabolic alkalosis, the following equations are used:[5]

• pCO2 = 0.7 [HCO3] + 20 mmHg +/- 5
• pCO2 = 0.7 [HCO3] + 21 mmHg

## References

1. Albert MS, Dell RB, Winters RW (February 1967). "Quantitative displacement of acid-base equilibrium in metabolic acidosis". Annals of Internal Medicine. 66 (2): 312–22. doi:10.7326/0003-4819-66-2-312. PMID 6016545.
2. Asch MJ, Dell RB, Williams GS, Cohen M, Winters RW (April 1969). "Time course for development of respiratory compensation in metabolic acidosis". The Journal of Laboratory and Clinical Medicine. 73 (4): 610–5. PMID 5775132.
3. "Case 1: Acid Base Tutorial, University of Connecticut Health Center". Retrieved 2009-05-09.
4. "Acid-Base Disorders: Acid-Base Regulation and Disorders". Merck Manual Professional. Retrieved 2009-05-09.
5. Hasan, Ashfaq. "The Analysis of Blood Gases." Handbook of Blood Gas/Acid-Base Interpretation. Springer London, 2013. pp. 253-266.